Annulus, fluid flow

This unit consists of two pipes or tubes, the smaller centered inside the larger as shown in Figure 10-92. One fluid flows in the annulus between the tubes the other flows inside the smaller tube. The heat transfer surface is considered as the outside surface of the inner pipe. The fluid film coefficient for the fluid inside the inner tube is determined the same as for any straight tube using Figures 10-46-10-52 or by the applicable relations correcting to the O.D. of the inner tube. For the fluid in the annulus, the same relations apply (Equation 10-47), except that the diameter, D, must be the equivalent diameter, D,.. The value of h obtained is applicable directly to the point desired — that is, the outer surface of the inner tube. ... 

Because the fluid flow in annular space is upward, the total bottom hole pressure is equal to the hydrostatic head plus the pressure loss in the annulus. Bottom hole pressure (psi). 

Stable Foam. When a well is drilled with stable foam as the drilling fluid, there is a back pressure valve at the blooey line. The back pressure valve allows for a continuous column of foam in the annulus while drilling operations are under way. Thus, while drilling, this foam column can have significant bottom-hole pressure. This bottomhole pressure can be sufficient to counter formation pore pressure and thus control potential production fluid flow into the well annulus. 

Aerated Mud. In aerated mud drilling operations, the drilling mud is injected with compressed air to lighten the mud. Therefore, at the bottom of the well in the annulus, the bottomhole pressure for an aerated mud will be less than that of the mud without aeration. However, an aerated mud drilling operation will have very significant bottomhole pressure capabilities and can easily be used to control potential production fluid flow into the well annulus. 

The gas is circulated by means of pressurised air. In airlift bioreactors, circulation is caused by die motion of injected gas through a central tube, with fluid recirculation through the annulus between die tube and the tower or vice versa. Figure 6.1 shows an airlift bioreactor widi an internal loop cycle of fluid flow. 

Pyrex jacket. The test fluid, distilled water, flowed vertically upwards through the annulus, while inside the heated tube a control fluid flowed which was either water or nitrogen gas, depending on the tube temperature required. 

The kinetic energy of the fluid flowing per unit time in the annulus between x and (. + ds) is given by ... 

Heat is to be transferred from one process stream to another by means of a double pipe heat exchanger. The hot fluid flows in a 1 in. sch 40 tube, which is inside (concentric with) a 2 in. sch 40 tube, with the cold fluid flowing in the annulus between the tubes. If both fluids are to flow at a velocity of 8 ft/s and the total equivalent length of the tubes is 1300 ft, what pump power is required to circulate the colder fluid Properties at average temperature p = 55 lbm/ft3, p = 8 cP. 

Consider a pipe of circular cross section with an inside and an outside diameter of d, and d0 respectively. Let this pipe be placed symmetrically inside a larger pipe having an inside diameter of D, and let a fluid flow through the annulus. Since the shear stress resisting the flow of fluid acts on both walls of the annulus, the appropriate flow perimeter required to calculate the equivalent diameter of the annulus de is (TrD,+nd0). Therefore... 

If flow is laminar with no radial or axial mixing (diffusion coefficient zero), we can write pit) finding p at each annulus that flows along the streamline in plug flow, as shown in Figure 8-4. From fluid mechanics we know that the velocity profile u(R) [really u,(R)] in laminar flow is given by the expression... 

The fluid flow rate through the entire annulus is given by... 

A typical double-pipe exchanger is shown in Fig. 2. It consists of two concentrically arranged pipes or tubes, with one fluid flowing in the inner pipe and the other in the annulus between the pipes. Special end fittings are used to get the fluids into and out of their respective flow channels and keep them from leaking to the atmosphere. Additional... 

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... 

The difference between the hydraulic radii for heat transfer and for fluid flow should be noted. In the preceding example, the correct equivalent diameter for evaluating friction due to the fluid flow in the annulus would be four times the cross-sectional flow area divided by the wetted perimeter, or 4 x(ttD /4-ttD /4)/(ttD2 + ttD = D2 - D,. 

Example 4.5 Entropy production in a flow through an annular packed bed The introduction of suitable packing into a fluid flow passage considerably enhances wall-to-fluid heat transfer, and hence reduces the entropy production due to heat transfer but increases the entropy production due to fluid-flow friction. Heat transfer to a fluid flowing in an annulus has a technical importance because we can heat or cool either or both of the surfaces independently. Entropy production provides a new criterion in analyzing such processes. In terms of the velocity and temperature profiles, the local rate of entropy production per unit volume of an incompressible Newtonian fluid for a two-dimensional annular flow is... 

Pressure drop due to fluid flow through a tube or annulus with or without packed beds can be calculated according to the following equation... 

Some simple heal transfer equipments consist of two concentric tubes, and are properly called double-tube heat exchangers (Fig. 8-27). In such devices, one fluid flows through the tube while the other flows through the aunular space. The governing differential equations for both flow.s are identical. I herefore, steady laminar flow through an annulus can he studied analytically by using suitable boundary conditions. 

Cell theory uses the concept of two concentric cylinders as the basis for modelling fluid flow through a porous solid simulated by an assembly of solid cylinders. The central of the two represents the soUd cylinder, the outer fluid flow enveloped by a free surface. The relative volume of the annulus to the central cylinder is taken as the same relative volume of fluid to solid in the assembly of cylinders. Navier-Stokes equations are then used to derive the reciprocal of k. Cell theory enables two basic cases to be considered fluid flow normal to the assembly of solid cylinders, and flow parallel to the axis of the cylinders. 

Since the annulus fluid velocity in the cross section is not the same, generally the velocity in the middle part of the drilling fluid is higher, carrying the particles back. And the velocity on both sides close to the drill pipe and the borehole fluid flow area is lower, making it difficult for the particles to be carried back. Therefore, the particle settling velocity Vp multiplied by the correction... 

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